Thin films of various materials are often used in the fabrication of semiconductor structures. The use of a laser to measure the radius of curvature of the surface of a semiconductor structure underneath a thin film is known in the art. Such a measurement is useful because the degree to which a thin film deforms the surface of a semiconductor structure, i.e. changes the local radius of curvature of the semiconductor structure, is indicative of the stress in the thin film. Thus, the measurement of the radius of curvature of a semiconductor structure is common, for example, in inspection of incoming wafers, as a monitor of the stability of a fabrication process, and for measurement of stress in a thin film.
The "cantilever beam" model, which is well known in the art, relates stress in a thin film to the material properties of the substrate (e.g. Young's modulus), the radius of curvature of the substrate, and the dimensions (e.g. thickness) of the thin film. Many techniques for measuring stress have been developed based on the cantilever beam model. Among these techniques are x-ray diffraction and laser reflection. A description of an x-ray diffraction technique may be found in an article entitled "Automatic x-ray diffraction measurement of the lattice curvature of substrate wafers for the determination of linear strain patterns" by A. Segmuller et al, J.Appl.Phys., volume 51, no. 12, December 1980, pp. 6224-30.
There are two principal types of laser reflection apparatuses--beam-splitting and scanning--for measuring radii of curvature. In either apparatus type, the radius of curvature is derived by measuring the angles of reflection of an incident laser beam at two or more points of known separation on the surface of the substrate.
In a beam-splitting type laser reflection apparatus, the laser beam is split optically into two or more beams directed at the two or more points at which angles of reflection are measured. An example of stress measurement performed with a beam-splitting type laser reflection apparatus is given in the article entitled "In situ stress measurements during thermal oxidation of silicon," E. Kobeda and E. A. Irene, J.Vac.Sci.Techno.B 7(2), Mar/Apr., 1989, pp. 163-66.
In a scanning type laser reflection apparatus, either the laser beam or the surface under measurement is moved from point to point in order that the angle of reflection may be measured at each selected point. Each of the following articles discusses stress measurements performed using a scanning type laser reflection apparatus:
i) "Principles and Applications of Wafer Curvature Techniques for Stress Measurements in Thin Films," P.A. Flinn in "Thin Films: Stresses and Mechanical Properties", MRS Proceedings, vol. 130, ed. Bravman, Nix, Barnett, Smith, 1989, pp. 41-51.
ii) "In situ stress measurement of refractory metal silicides during sintering," J.T. Pan and I. Blech, J.Appl.Phys. 55(8), April 1984, pp. 2874-80.
iii) "Thermal stresses and cracking resistance of dielectric films (SiN, Si.sub.3 N.sub.4, and SiO.sub.2) on Si Substrates," A. K. Sinha et al., J.App.Phys. 49(4), April 1978, pp. 2423-26.
The references cited above are also illustrative of the method of stress measurement.
Because a monochromatic (i.e., one single wavelength) laser is used in either type of laser reflection stress measurement apparatuses, an apparatus in the prior art is unable to provide a reliable measurement under certain conditions. These conditions are illustrated in FIG. 1.
FIG. 1 shows a thin film t under measurement bounded by media 1 and 2 at the upper and lower surfaces of the thin film. Reflected beams a and b of incident laser beam I are shown to reflect respectively from the upper and lower interfaces (i.e. the interfaces between medium 1 and thin film t, and between medium 2 and thin film t). The reflected beams a and b will destructively interfere with each other, i.e., cancel each other, when the following conditions are satisfied: (i) the thin film's index of refraction .mu..sub.t is close to the quantity .sqroot..mu..sub.1 .mu..sub.2, which is the geometrical mean of media 1 and 2's individual indices of refraction (.mu..sub.1, .mu..sub.2 ; and, (ii) the thickness of the film is such that the two beams reflected from its two interfaces with the bounding media are out of phase by one-half wavelength. Condition (ii) is satisfied when EQU d=(.lambda./n)/4+m(.lambda./n)/2 (1)
where .lambda. is the wavelength of the incident beam in air,
d is the thickness of the thin film, PA1 n is the index of refraction of the thin film, and PA1 m is any integer greater than or equal to zero.
When both conditions (i) and (ii) are satisfied, the reflected beams at the interfaces destructively interfere or cancel each other resulting in either no intensity detectable or substantially diminished intensity detectable in the reflected beams.
For example, a thin film particularly difficult to measure in practice is silicon nitride, which has a refractive index of about 2, when bounded by air (refractive index of 1) and silicon (refractive index of about 4). In this example, since the index of refraction for silicon nitride is about 2, beams a and b at the respective air/silicon nitride and silicon nitride/silicon interfaces cancel each other in the manner described above, when the thickness of the thin film is one-quarter of the wavelength of the incident beam in silicon nitride, or at one-half wavelength increments thereof.
Thus, an apparatus and method capable of avoiding poor measurement of the angle of reflection due to destructive interference over a wide range of thicknesses using existing laser technology is desired.